Larotonda spaces: Homogeneous spaces and conditional expectations

RECHT, LÁZARO; ANDRUCHOW, ESTEBAN

INTERNATIONAL JOURNAL OF MATHEMATICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2016 vol. 27

0129-167X

We define a Larotonda space as a quotient space = of the unitary groups of C-algebras 1 with a faithful unital conditional expectation. In particular, is complemented in , a fact which implies that has C∞ differentiable structure, with the topology induced by the norm of . The conditional expectation also allows one to define a reductive structure (in particular, a linear connection) and a -invariant Finsler metric in . Given a point and a tangent vector X (T), we consider the problem of whether the geodesic of the linear connection satisfying these initial data is (locally) minimal for the metric. We find a sufficient condition. Several examples are given, of locally minimal geodesics.